A Profile of Mathematical Logic

by Howard DeLong

Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and the imagination, it profiles the development of logic from ancient to modern times and compellingly examines the nature of logic and its philosophical implications. No prior knowledge of logic is necessary; readers need only an acquaintance with high school mathematics. The author emphasizes understanding, rather than technique, and focuses on such topics as the historical reasons for the formation of Aristotelian logic, the rise of mathematical logic after more than 2,000 years of traditional logic, the nature of the formal axiomatic method and the reasons for its use, and the main results of metatheory and their philosophic import. The treatment of the Gödel metatheorems is especially detailed and clear, and answers to the problems appear at the end.

Genres: Mathematics, Philosophy, Logic, Science, Nonfiction

336 pages, Paperback

First published January 1, 2004

Reviews

[Bria]

"All this may perhaps be made clear by an analogy: Assume (as in a now-old-fashioned theology) that Adam and Eve are literally the first two humans (initial formulas) and that a property which they share—original sin (property of the initial formulas)—is hereditary and that thus all their
descendants (theorems) share it. The existence of a human without that property—Jesus (a formula)—saves humanity (the system) from damnation (inconsistency). This is so because we know that if all humans (formulas) are descended (inferred) from Adam and Eve (initial formulas), then mankind (the system) is doomed (inconsistent)."

This probably would have done a great job teaching me logic if my brain wasn't completely rotting in my head, but at least moving my eyes over the words felt kinda nice.

[Yvan Moses Levy · Rating 4 out of 5]

I recommend this book for the beginning.

A very precious book.

But The definitions are brought in between long sentences and are not highlighted well enough. And sometimes are omitted or are vague allusions by the way.

The Propositional Calculus is well explained.

The exercises are very entertaining and each of them is well answered.

The philosophical side is clear and interesting.

The prose is pleasant and friendly for people who are worrying in the mathematical world.

I see this book as one of the first steps for the students who is not able to dive directly into rigorous books.

I'm grateful for the author for this.